Research Papers: Multiphase Flows

Measurements of Loading and Tip Vortex Due to High-Reynolds Number Flow Over a Rigid Lifting Surface

[+] Author and Article Information
Michael H. Krane, Richard S. Meyer, Matthew J. Weldon, Brian Elbing, David W. DeVilbiss

Applied Research Laboratory,
Penn State University,
State College, PA 16804

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 25, 2013; final manuscript received February 1, 2015; published online March 19, 2015. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 137(7), 071301 (Jul 01, 2015) (9 pages) Paper No: FE-13-1340; doi: 10.1115/1.4029723 History: Received May 25, 2013; Revised February 01, 2015; Online March 19, 2015

An experimental study of high-Reynolds number flow over a rigid hydrofoil (David Taylor model basin (DTMB) modified NACA66-009, rectangular planform, aspect ratio (AR = 4, square tip) is presented. The measurements were performed in the Garfield Thomas Water Tunnel at Applied Research Laboratory (ARL) Penn State. Load measurements were performed at ReC = 1.5 × 106 and 2.4 × 106, for angles of attack between −8 deg and +8 deg. Measurements of three components of velocity were performed using stereo particle image velocimetry (SPIV) on a cross-flow plane to resolve the tip vortex flow 0.42 chord lengths downstream of the trailing edge, for four angles of attack ranging from 0.5 deg to 3.5 deg. Nondimensional tip vortex circulation varied weakly with angle of attack. Vortex location in the plane of measurement, relative to the trailing edge, was unchanged for the ranges studied, though the vortex core grew in size with angle of attack. These results are consistent with the finding that the net lift force acts between 45% and 46% span, measured from the root, in that any angle of attack variations in tip vortex strength or radius result in minimal changes in spanwise loading distribution.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Green, S. I., 1995, Fluid Vortices, Kluwer Academic Publishers, Boston, MA/Dordrecht. [CrossRef]
Dacles-Mariani, J., Zilliac, G. G., Chow, J. S., and Bradshaw, P., 1995, “Numerical/Experimental Study of a Wingtip Vortex in the Near Field,” AIAA J., 33(9), pp. 1561–1568. [CrossRef]
Stinebring, D. R., Farrell, K. J., and Billet, M. L., 1991, “The Structure of a Three-Dimensional Tip Vortex at High Reynolds Numbers,” ASME J. Fluids Eng., 113(3), pp. 496–503. [CrossRef]
Green, S. I., and Acosta, A. J., 1991, “Unsteady Flow in Trailing Vortices,” J. Fluid Mech., 227, pp. 107–134. [CrossRef]
Shekarriz, A., Fu, T. C., Katz, J., Liu, H. L., and Huang, T. T., 1992, “Study of Junction and Tip Vortices Using Particle Displacement Velocimetry,” AIAA J., 30(1), pp. 145–152. [CrossRef]
Shekarriz, A., Fu, T. C., Katz, J., Liu, H. L., and Huang, T. T., 1993, “Near-Field Behavior of a Tip Vortex,” AIAA J., 31(1), pp. 112–118. [CrossRef]
Devenport, W. J., Rife, M. C., Liapis, S. I., and Follin, G. J., 1996, “The Structure and Development of a Wing-Tip Vortex,” J. Fluid Mech., 312, pp. 67–106. [CrossRef]
Chow, J. S., Zilliac, G. G., and Bradshaw, P., 1997, “Mean and Turbulence Measurements in the Near Field of a Wingtip Vortex,” AIAA J., 35(10), pp. 1561–1567. [CrossRef]
Ramaprian, B. R., and Zheng, Y., 1997, “Measurements in Rollup Region of the Tip Vortex From a Rectangular Wing,” AIAA J., 35(12), pp. 1837–1843. [CrossRef]
Birch, D., Lee, T., Mokhtarian, F., and Kafyeke, F., 2003, “Rollup and Near-Filed Behavior of a Tip Vortex,” J. Aircr., 40(3), pp. 603–607. [CrossRef]
Birch, D., Lee, T., Mokhtarian, F., and Kafyeke, F., 2004, “Structure and Induced Drag of a Tip Vortex,” J. Aircr., 41(5), pp. 1138–1145. [CrossRef]
Heyes, A. L., Hubbard, S. J., Marquis, A. J., and Smith, D. A., 2003, “On the Roll-Up of a Trailing Vortex Sheet in the Very Near Field,” Proc. Inst. Mech. Eng., Part G, 217(5), pp. 263–269. [CrossRef]
Zhang, H. J., Zhou, Y., and Whitelaw, J. H., 2006, “Near-Field Wing-Tip Vortices and Exponential Vortex Solution,” AIAA J., 43(2), pp. 445–449. [CrossRef]
Iungo, G. V., Skinner, P., and Burseti, G., 2009, “Correction of Wandering Smoothing Effects on Static Measurements of a Wing-Tip Vortex,” Exp. Fluids, 46(3), pp. 435–452. [CrossRef]
Arndt, R. E. A., and Keller, A. P., 1992, “Water Quality Effects on Cavitation Inception in a Trailing Vortex,” ASME J. Fluids Eng., 114(3), pp. 430–438. [CrossRef]
Arndt, R. E. A., Arakeri, V. H., and Higuchi, H., 1991, “Some Observations of Tip-Vortex Cavitation,” J. Fluid Mech., 229, pp. 269–289. [CrossRef]
Gerontakos, P., and Lee, T., 2006, “Near-Field Tip Vortex Behind a Swept Wing Model,” Exp. Fluids, 40(1), pp. 141–155. [CrossRef]
Beresh, S. J., Henfling, J. F., and Spillers, R. W., 2009, “Planar Velocimetry of a Fin Trailing Vortex in Subsonic Compressible Flow,” AIAA J., 47(7), pp. 1730–1740. [CrossRef]
Beresh, S. J., Smith, J. A., Henfling, J. F., Grasser, T. W., and Spillers, R. W., 2009, “Interaction of a Fin Trailing Vortex With a Downstream Control Surface,” J. Spacecr. Rockets, 46(2), pp. 318–328. [CrossRef]
Elsayed, O. A., Asrar, W., Omar, A. A., and Kwon, K., 2012, “Evolution of NACA23012 Wake Vortices Structure Using PIV,” ASCE J. Aerosp. Eng., 25(1), pp. 10–20. [CrossRef]
Lehman, A. F., 1959, “The Garfield Thomas Water Tunnel,” Applied Research Laboratory, The Pennsylvania State University (ARL Penn State), Reston, VA, Technical Report No. NORD 16597-56.
Marboe, R. C., Weyer, R. M., and Jonson, M. L., 1993, “Hydroacoustic Research Capabilities in the Large Water Tunnel at ARL-Penn State,” Symposium on Flow Noise Modeling, Measurement, and Control, New Orleans, LA, Nov. 28–Dec. 3, NCA-VOL 15/FED-VOL 168, pp. 125–135.
Robbins, B. E., 1978, “Water Tunnel Turbulence Measurements Behind a Honeycomb,” J. Hydronautics, 12(3), pp. 122–128. [CrossRef]
Brockett, T., 1966, “Minimum Pressure Envelopes for Modified NACA-66 Sections With a = 0.8 and BuShips Type I and Type II Sections,” David W. Taylor Naval Ship Research and Development Center, Report No. 1780.
Lawson, N., and Wu, J., 1997, “Three-Dimensional Particle Image Velocimetry: Experimental Error Analysis of a Digital Angular Stereoscopic System,” Meas. Sci. Technol., 8(12), pp. 1455–1464. [CrossRef]
Rae, W. H.Jr., and Pope, A., 1984, Low-Speed Wind Tunnel Testing, 2nd ed., Wiley, Somerset, NJ.
Anderson, J., 2001, Fundamentals of Aerodynamics, 3rd ed., McGraw-Hill, New York.
Batchelor, G. K., 1964, “Axial Flow in Trailing Line Vortices,” J. Fluid Mech., 20(4), pp. 645–658. [CrossRef]


Grahic Jump Location
Fig. 1

Installation of the hydrofoil (fin) in the Garfield Thomas Water Tunnel test section (1219 mm diameter). (a) Cutaway shows flat wall liner and windows offering optical access. Coordinate axes are also shown. (b) Detail of hydrofoil installation, showing load cell and location of SPIV measurement plane.

Grahic Jump Location
Fig. 2

SPIV setup used to characterize the tip vortex flow

Grahic Jump Location
Fig. 3

Angle-of-attack variation of the load coefficients for rigid fin, ◇—lift coefficient, CL; ◻—drag coefficient, CD; Δ—pitch moment about 1/4-chord, CMZ; o—roll moment, CMX; empty symbols: ReC = 1.5 × 106, and solid symbols: ReC = 2.4 × 106

Grahic Jump Location
Fig. 4

Variation of spanwise lift point of application ZL/b with angle of attack, empty symbols—ReC = 1.5 × 106, filled symbols—2.4 × 106. Dashed lines indicate vertical and horizontal asymptotes: vertical asymptote is at α = −2.67 deg, the zero-lift angle of attack, at which ZL/b is singular. Horizontal asymptotes are located at approximately ZL/b = 0.45 and 0.47, for ReC = 2.4 × 106 and 1.5 × 106, respectively.

Grahic Jump Location
Fig. 5

Tip vortex flow on cross-flow plane, 0.42 c downstream of hydrofoil trailing edge, viewed from upstream. (a) α = 0.5 deg, (b) α = 2.5 deg, (c) α = 3.0 deg, and (d) α = 3.5 deg. Left column: velocity vectors superimposed on shading indicating axial velocity component. Right column: velocity vectors superimposed on shading indicating axial vorticity. Dark line denotes location of hydrofoil trailing edge, located below Y/c = 0 for α > 0 deg. Tip/trailing edge corner is located at Y/c = 0, Z/c = 2 for α = 0 deg.

Grahic Jump Location
Fig. 6

Scatter plots showing profiles of velocity and vorticity in the tip vortex flow at 0.42 c downstream of the trailing edge (for the lifting surface at zero angle of attack). Each grouping of three plots corresponds to a particular angle of attack, and shows (1) transverse velocity profiles Uy/U versus (ZZv)/c (*) and −Uz/U versus (Y − Yv)/c (o); (2) axial of velocity velocity Ux/U versus (Z − Zv)/c (Δ); and (3) axial vorticity ωx rc2/Γ versus both (Z − Zv)/c (o) and (Y − Yv)/c (*). (a) α = 0.5 deg, (b) α = 2.5 deg, (c) α = 3.0 deg, and (d) α = 3.5 deg.

Grahic Jump Location
Fig. 7

Estimation of tip vortex circulation, α = 3.5 deg. Plot shows estimated circulation versus length of side of square integration path around the tip vortex center. When tip vortex is contained, estimated circulation increases with contour size, because of axial vorticity in wing wake, though at a slower rate than when the contour does not fully contain the vortex. The location of slope change is taken to indicate the tip vortex circulation, as well as vortex core size.

Grahic Jump Location
Fig. 8

Tip vortex behavior, deduced from SPIV measurements shown in Fig. 5. (a) vortex circulation normalized by average wing circulation and (b) vortex core size, normalized by chord length. Small variations in tip vortex strength (relative to wing circulation) and location suggest that the effect of tip flow on lift distribution depends weakly on angle of attack.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In